Simple Interest The simple interest on an investment is...

Simple Interest The simple interest on an investment
is directly proportional to the amount of the investment.
An investment of $\$ 6500$ will earn $\$ 211.25$ after 1 year.
Find a mathematical model that gives the interest $I$ after
1 year in terms of the amount invested $P .$

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Key Concepts

Simple Interest

This concept refers to the calculation of interest where the interest earned over a period is computed as a fixed percentage of the principal amount. Simple interest does not compound, meaning the interest is not reinvested to earn additional interest. In finance, the formula is commonly given as I = P × r, where I is the interest, P is the principal, and r is the rate of interest per time period.

Direct Proportionality

Direct proportionality is a relationship between two variables in which one variable is a constant multiple of the other. In the context of simple interest, this means that the interest earned is directly proportional to the amount invested, implying that if the principal amount increases, the interest increases linearly and vice versa.

Mathematical Modeling

Mathematical modeling involves creating mathematical representations of real-world situations. In finance and interest calculations, it entails setting up equations based on known data to predict or analyze outcomes. In this context, it means forming a linear equation that relates the interest earned in one year to the amount invested, using given data to determine the constant of proportionality which represents the interest rate.

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